seminars/seminar8/seminar8.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Семинар 6. Степенной метод. QR алгоритм"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Экспериментально посмотрим на сходимость степенного метода\n",
    "\n",
    "$$x_{k+1} = \\frac{Ax_k}{\\|Ax_k\\|} $$\n",
    "\n",
    "- Теоретическая скорость сходимости **линейная** с фактором $\\frac{|\\lambda_2|}{|\\lambda_1|}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def power_method(A, x0, max_iter, eps):\n",
    "    x = x0.copy()\n",
    "    conv = [x]\n",
    "    for i in range(max_iter):\n",
    "        x = A @ x\n",
    "        x = x / np.linalg.norm(x)\n",
    "        conv.append(x)\n",
    "        eigval = x @ (A @ x)\n",
    "        res = A @ x - eigval * x\n",
    "        if np.linalg.norm(res) < eps:\n",
    "            break\n",
    "    return x, eigval, conv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Симметричная положительно определённая матрица"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[9.08050598e-05 5.98738933e-03 9.44215434e-02 3.69030606e-01\n",
      " 4.09806706e-01 4.55736343e-01 9.08505859e-01 1.33621119e+00\n",
      " 1.41027596e+00 1.85518946e+00 2.86702867e+00 3.18195816e+00\n",
      " 3.67297697e+00 4.33200403e+00 4.87305139e+00 5.84238777e+00\n",
      " 7.22920186e+00 7.92468749e+00 8.25763141e+00 9.77947698e+00\n",
      " 1.02729795e+01 1.17100102e+01 1.23221010e+01 1.29426268e+01\n",
      " 1.57507249e+01 1.67271149e+01 1.69323290e+01 1.83603872e+01\n",
      " 1.92439586e+01 2.11926036e+01 2.33119037e+01 2.44001004e+01\n",
      " 2.68565712e+01 2.78273001e+01 3.07023785e+01 3.17923926e+01\n",
      " 3.32659145e+01 3.61619443e+01 3.66202382e+01 4.05640198e+01\n",
      " 4.12172214e+01 4.20182719e+01 4.40093414e+01 4.59955289e+01\n",
      " 4.91454558e+01 5.25278841e+01 5.36208303e+01 5.66290426e+01\n",
      " 6.11072508e+01 6.36642417e+01 6.67790025e+01 7.18717500e+01\n",
      " 7.53102151e+01 7.69637054e+01 8.05181031e+01 8.42937297e+01\n",
      " 8.66480959e+01 9.06328877e+01 9.70358984e+01 9.91344601e+01\n",
      " 1.02186114e+02 1.04807972e+02 1.06496298e+02 1.08614964e+02\n",
      " 1.11090944e+02 1.13312973e+02 1.18720769e+02 1.20750359e+02\n",
      " 1.23550954e+02 1.30529961e+02 1.33110578e+02 1.35966976e+02\n",
      " 1.43842411e+02 1.48188571e+02 1.50408079e+02 1.59122894e+02\n",
      " 1.62032721e+02 1.67318915e+02 1.75543243e+02 1.80285225e+02\n",
      " 1.84403301e+02 1.92881856e+02 1.96656774e+02 1.99615005e+02\n",
      " 2.05961924e+02 2.14641170e+02 2.30927812e+02 2.35597988e+02\n",
      " 2.43338837e+02 2.52579082e+02 2.56604444e+02 2.65129750e+02\n",
      " 2.77871455e+02 2.80462621e+02 2.93534013e+02 3.03008749e+02\n",
      " 3.18527621e+02 3.27428431e+02 3.34944513e+02 3.75195330e+02]\n",
      "[[-0.06016232 -0.16739279  0.07882162 ...  0.16435344 -0.07348767\n",
      "   0.20149496]\n",
      " [ 0.02201546 -0.01411542 -0.04828668 ...  0.03479458 -0.11934563\n",
      "  -0.02111148]\n",
      " [ 0.04369109 -0.05991018  0.09989582 ...  0.10143244  0.12899659\n",
      "  -0.21137303]\n",
      " ...\n",
      " [-0.08912264  0.00629706  0.10026867 ...  0.04131496 -0.0365003\n",
      "   0.14639525]\n",
      " [ 0.0531173   0.08423888 -0.03214335 ... -0.06350376  0.04537541\n",
      "   0.25276245]\n",
      " [ 0.23780225 -0.09296552 -0.11421212 ... -0.03133326 -0.06324955\n",
      "  -0.01112604]]\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(0)\n",
    "n = 100\n",
    "A = np.random.randn(n, n)\n",
    "A = A.T @ A\n",
    "\n",
    "true_eigvals, true_eigvec = np.linalg.eigh(A)\n",
    "print(true_eigvals)\n",
    "print(true_eigvec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.20149504  0.02111166  0.21137266 -0.01086659 -0.00780266 -0.03149369\n",
      "  0.03317797 -0.10571077  0.05631894 -0.00708571 -0.2345815  -0.0323832\n",
      "  0.02293809 -0.1030258   0.17442166  0.1414175   0.06648175  0.10508005\n",
      "  0.21889482  0.02946043  0.03890899  0.07901664 -0.01098292 -0.00222161\n",
      "  0.02816873  0.14741542  0.05526265 -0.16585199 -0.16786561  0.00702125\n",
      " -0.00512802  0.053801    0.08472981  0.04250767 -0.043731   -0.02308412\n",
      " -0.03098449  0.01041469  0.08245142  0.07971054 -0.09226347 -0.09864837\n",
      "  0.16299778 -0.11417104  0.00056612 -0.09476633  0.10988122 -0.09608952\n",
      "  0.09752086  0.0720101   0.01995432 -0.08523925  0.11743321  0.03655672\n",
      "  0.05399115  0.2372778   0.02466907  0.00672446 -0.01103931 -0.05729322\n",
      " -0.00972008 -0.0079006  -0.04444629 -0.01459691 -0.07719303  0.1637581\n",
      "  0.11115478  0.19175726 -0.13649498  0.00392001 -0.18193311 -0.09988945\n",
      " -0.02479226  0.11426804  0.14887836  0.03728107 -0.00812182  0.07419095\n",
      " -0.00108646  0.06527702  0.17841344  0.15647811  0.05655328  0.14757923\n",
      " -0.05938854 -0.12013571 -0.01959283  0.13167542  0.00537669 -0.07184117\n",
      "  0.00743083 -0.03536772  0.03040508  0.00793515  0.01899831  0.05746055\n",
      " -0.04960624 -0.14639524 -0.25276245  0.01112619]\n",
      "375.19533026493616\n"
     ]
    }
   ],
   "source": [
    "x0 = np.random.randn(n)\n",
    "max_eigvec, max_eigval, conv = power_method(A, x0, 100, 1e-6)\n",
    "print(max_eigvec)\n",
    "print(max_eigval)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.rc(\"text\", usetex=True)\n",
    "\n",
    "power_method_eigval_conv = np.array([np.linalg.norm(A @ x - x @ (A @ x) * x) for x in conv])\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(power_method_eigval_conv, linewidth=4, label=\"Eigval conv\")\n",
    "power_method_eigvec_conv = np.array([np.linalg.norm(x - x[0] / true_eigvec[0, -1] * true_eigvec[:, -1]) for x in conv])\n",
    "plt.plot(power_method_eigvec_conv, linewidth=4, label=\"Eigvec conv\")\n",
    "plt.legend(fontsize=20)\n",
    "plt.yscale(\"log\")\n",
    "plt.ylabel(\"Residual norm\", fontsize=20)\n",
    "plt.yticks(fontsize=16)\n",
    "plt.xlabel(\"\\# iterations\", fontsize=20)\n",
    "plt.xticks(fontsize=16)\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.00111126 0.76334892 0.77052966 0.78185062 0.79891308 0.81791715\n",
      " 0.83491388 0.84772505 0.85626571 0.86152633 0.86463942 0.86647893\n",
      " 0.86761034 0.86836437 0.86892173 0.86937599 0.86977319 0.87013476\n",
      " 0.87047004 0.87078285 0.87107473 0.87134649 0.87159886 0.87183274\n",
      " 0.87204924 0.87224961 0.87243524 0.87260753 0.87276791 0.87291776\n",
      " 0.87305838 0.87319102 0.87331682 0.87343685 0.87355206 0.87366334\n",
      " 0.87377149 0.87387723 0.8739812  0.874084   0.87418613 0.87428809\n",
      " 0.87439029 0.87449311 0.87459691 0.87470199 0.87480864 0.8749171\n",
      " 0.87502763 0.87514041 0.87525565 0.87537351 0.87549416 0.87561773\n",
      " 0.87574437 0.87587417 0.87600725 0.8761437  0.8762836  0.87642702\n",
      " 0.87657402 0.87672465 0.87687895 0.87703694 0.87719864 0.87736406\n",
      " 0.87753319 0.87770602 0.87788251 0.87806263 0.87824633 0.87843354\n",
      " 0.8786242  0.87881821 0.87901548 0.8792159  0.87941935 0.8796257\n",
      " 0.87983481 0.88004652 0.88026067 0.8804771  0.88069561 0.88091602\n",
      " 0.88113813 0.88136174 0.88158663 0.88181259 0.8820394  0.88226682\n",
      " 0.88249463 0.88272261 0.88295051 0.88317811 0.88340518 0.88363149\n",
      " 0.8838568  0.88408091 0.8843036  0.88452464]\n",
      "[0.09376068 0.89732463 0.90166615 0.90645306 0.90482449 0.89995928\n",
      " 0.89438266 0.88920835 0.88482032 0.8812833  0.87852906 0.87644119\n",
      " 0.87489502 0.87377562 0.87298483 0.87244252 0.87208528 0.871864\n",
      " 0.87174125 0.87168891 0.87168605 0.8717173  0.87177144 0.87184041\n",
      " 0.87191849 0.87200166 0.87208721 0.87217331 0.87225882 0.87234308\n",
      " 0.87242576 0.87250678 0.87258622 0.87266425 0.87274115 0.8728172\n",
      " 0.87289273 0.87296809 0.87304362 0.87311964 0.87319648 0.87327447\n",
      " 0.87335391 0.8734351  0.87351833 0.87360386 0.87369196 0.87378289\n",
      " 0.87387689 0.87397419 0.87407503 0.87417961 0.87428816 0.87440087\n",
      " 0.87451794 0.87463955 0.87476588 0.8748971  0.87503336 0.87517482\n",
      " 0.87532162 0.87547388 0.87563171 0.87579522 0.8759645  0.87613962\n",
      " 0.87632063 0.87650758 0.8767005  0.87689937 0.8771042  0.87731494\n",
      " 0.87753154 0.87775393 0.87798199 0.87821561 0.87845464 0.87869891\n",
      " 0.87894824 0.87920239 0.87946114 0.87972423 0.87999137 0.88026226\n",
      " 0.88053657 0.88081397 0.88109411 0.8813766  0.88166107 0.88194712\n",
      " 0.88223434 0.88252233 0.88281067 0.88309894 0.88338671 0.88367359\n",
      " 0.88395916 0.88424301 0.88452475 0.884804  ]\n",
      "0.8927203671453576\n"
     ]
    }
   ],
   "source": [
    "print(power_method_eigval_conv[1:] / power_method_eigval_conv[:-1])\n",
    "print(power_method_eigvec_conv[1:] / power_method_eigvec_conv[:-1])\n",
    "print(true_eigvals[-2] / true_eigvals[-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Симметричная матрица\n",
    "\n",
    "- Cобственные значений вещественные"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-8.61048661 -3.85659192 -2.54678979 -0.27970044  0.9388054   2.18655001\n",
      "  2.73246746  4.08978992  5.30115507  7.08889719]\n",
      "[[-0.25513076 -0.06252921 -0.0692556  -0.52676901 -0.43543543 -0.09169641\n",
      "   0.5912155   0.21516116  0.22230254 -0.07386281]\n",
      " [ 0.22245595  0.27523843 -0.42968365  0.29042369 -0.60920005 -0.11024123\n",
      "  -0.13673533  0.33696833 -0.27131146  0.12903974]\n",
      " [-0.31804172  0.02659569 -0.06607188  0.00385438 -0.37662599  0.22565677\n",
      "   0.02436865 -0.77597881 -0.28167364  0.13753796]\n",
      " [-0.49401161 -0.09392092  0.26477529  0.09385435 -0.12687791 -0.73787128\n",
      "  -0.30682621  0.02975823 -0.08031053 -0.07865824]\n",
      " [ 0.26551038 -0.12734143  0.04624029 -0.24253592 -0.38432658  0.07464717\n",
      "  -0.55752365 -0.16820583  0.56667201 -0.19698848]\n",
      " [-0.41122551  0.41704327 -0.15409232 -0.38398684  0.1846518   0.18976975\n",
      "  -0.37519098  0.19941191  0.09051752  0.47638482]\n",
      " [-0.08832906 -0.44493863  0.37562437  0.32253412 -0.23013891  0.23840742\n",
      "   0.0438475   0.21511463  0.17682481  0.59986643]\n",
      " [ 0.20369759  0.67158788  0.67183872  0.03131935 -0.15807738 -0.02359862\n",
      "   0.15024922 -0.05617545  0.05257644  0.03299547]\n",
      " [ 0.32369565 -0.26769409  0.27253283 -0.55208046 -0.06016722 -0.00980033\n",
      "  -0.18265787  0.09848741 -0.61973184  0.1168189 ]\n",
      " [ 0.38281569  0.00192739 -0.20853415 -0.11521038  0.13397934 -0.53384253\n",
      "   0.1660401  -0.33157396  0.20921858  0.55898764]]\n"
     ]
    }
   ],
   "source": [
    "n = 10\n",
    "A = np.random.randn(n, n)\n",
    "A = A + A.T\n",
    "true_eigvals, true_eigvec = np.linalg.eigh(A)\n",
    "print(true_eigvals)\n",
    "print(true_eigvec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.25513075 -0.22245595  0.31804173  0.4940116  -0.2655104   0.41122554\n",
      "  0.0883291  -0.20369759 -0.32369565 -0.38281565]\n",
      "-8.610486614573762\n"
     ]
    }
   ],
   "source": [
    "x0 = np.random.randn(n)\n",
    "max_eigvec, max_eigval, conv = power_method(A, x0, 500, 1e-6)\n",
    "print(max_eigvec)\n",
    "print(max_eigval)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "power_method_eigval_conv = np.array([np.linalg.norm(A @ x - x @ (A @ x) * x) for x in conv])\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(power_method_eigval_conv, linewidth=4, label=\"Eigval conv\")\n",
    "\n",
    "idx = np.argmax(np.abs(true_eigvals))\n",
    "\n",
    "power_method_eigvec_conv = np.array([np.linalg.norm(x - x[0] / true_eigvec[0, idx] * true_eigvec[:, idx]) for x in conv])\n",
    "plt.plot(power_method_eigvec_conv, linewidth=4, label=\"Eigvec conv\")\n",
    "plt.legend(fontsize=20)\n",
    "plt.yscale(\"log\")\n",
    "plt.ylabel(\"Residual norm\", fontsize=20)\n",
    "plt.yticks(fontsize=16)\n",
    "plt.xlabel(\"\\# iterations\", fontsize=20)\n",
    "plt.xticks(fontsize=16)\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.35663948 1.20673238 0.92789305 0.82360616 0.79543551 0.79531096\n",
      " 0.80303133 0.81069293 0.81617412 0.81956537 0.8214895  0.82251284\n",
      " 0.82302406 0.82325975 0.82335449 0.82338129 0.82337818 0.82336405\n",
      " 0.82334769 0.82333281 0.82332059 0.82331112 0.82330403 0.82329885\n",
      " 0.82329513 0.82329249 0.82329063 0.82328934 0.82328844 0.82328782\n",
      " 0.8232874  0.82328711 0.82328691 0.82328677 0.82328668 0.82328661\n",
      " 0.82328657 0.82328654 0.82328652 0.82328651 0.8232865  0.82328649\n",
      " 0.82328649 0.82328648 0.82328648 0.82328648 0.82328648 0.82328648\n",
      " 0.82328648 0.82328648 0.82328648 0.82328648 0.82328648 0.82328648\n",
      " 0.82328648 0.82328648 0.82328648 0.82328648 0.82328648 0.82328648\n",
      " 0.82328648 0.82328648 0.82328648 0.82328648 0.82328648 0.82328648\n",
      " 0.82328648 0.82328648 0.82328648 0.82328648 0.82328648 0.82328648\n",
      " 0.82328648 0.82328648 0.82328648 0.82328648 0.82328648 0.82328648\n",
      " 0.82328648 0.82328648 0.82328648 0.82328648 0.82328648]\n",
      "[0.24057804 0.79808784 0.60340714 0.69333955 0.70024188 0.75020187\n",
      " 0.77677425 0.79971512 0.81314546 0.82026481 0.82401317 0.82530794\n",
      " 0.82576574 0.82558593 0.82530085 0.82492425 0.82459884 0.82430602\n",
      " 0.82407435 0.8238864  0.82374223 0.82363013 0.82354533 0.8234807\n",
      " 0.82343213 0.8233955  0.82336806 0.82334746 0.82333207 0.82332054\n",
      " 0.82331193 0.82330549 0.82330068 0.82329709 0.8232944  0.8232924\n",
      " 0.8232909  0.82328978 0.82328895 0.82328832 0.82328786 0.82328751\n",
      " 0.82328725 0.82328705 0.82328691 0.8232868  0.82328672 0.82328666\n",
      " 0.82328661 0.82328658 0.82328655 0.82328653 0.82328652 0.82328651\n",
      " 0.8232865  0.82328649 0.82328649 0.82328649 0.82328648 0.82328648\n",
      " 0.82328648 0.82328648 0.82328648 0.82328648 0.82328648 0.82328648\n",
      " 0.82328648 0.82328648 0.82328648 0.82328648 0.82328648 0.82328648\n",
      " 0.82328648 0.82328648 0.82328648 0.82328648 0.82328648 0.82328648\n",
      " 0.82328648 0.82328648 0.82328648 0.82328648 0.82328648]\n",
      "0.8232864765107001\n"
     ]
    }
   ],
   "source": [
    "print(power_method_eigval_conv[1:] / power_method_eigval_conv[:-1])\n",
    "print(power_method_eigvec_conv[1:] / power_method_eigvec_conv[:-1])\n",
    "sorted_abs_eigvals = np.sort(np.abs(true_eigvals))\n",
    "print(sorted_abs_eigvals[-2] / sorted_abs_eigvals[-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Несимметричная матрица"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-2.16876059+2.36653506j -2.16876059-2.36653506j  0.88057471+2.64153395j\n",
      "  0.88057471-2.64153395j  1.71045255+0.35258153j  1.71045255-0.35258153j\n",
      " -0.99410388+0.68827313j -0.99410388-0.68827313j  0.17116704+0.6820587j\n",
      "  0.17116704-0.6820587j ]\n",
      "[0.70320853 0.70320853 1.20911638 1.20911638 1.74641395 1.74641395\n",
      " 2.78444131 2.78444131 3.20998608 3.20998608]\n",
      "[[ 0.26657508-0.00200193j  0.26657508+0.00200193j -0.1438417 +0.05898648j\n",
      "  -0.1438417 -0.05898648j  0.11084996+0.09270145j  0.11084996-0.09270145j\n",
      "   0.15835992+0.04108055j  0.15835992-0.04108055j  0.03134198+0.1275214j\n",
      "   0.03134198-0.1275214j ]\n",
      " [-0.19870309+0.27887529j -0.19870309-0.27887529j -0.61828967+0.j\n",
      "  -0.61828967-0.j          0.0760079 +0.10777555j  0.0760079 -0.10777555j\n",
      "  -0.12089131-0.28436715j -0.12089131+0.28436715j  0.26348093-0.10963247j\n",
      "   0.26348093+0.10963247j]\n",
      " [-0.19429107+0.06731809j -0.19429107-0.06731809j -0.01377608-0.04949236j\n",
      "  -0.01377608+0.04949236j  0.34014524+0.13915111j  0.34014524-0.13915111j\n",
      "  -0.08622701-0.01223905j -0.08622701+0.01223905j -0.08031648-0.08244874j\n",
      "  -0.08031648+0.08244874j]\n",
      " [-0.01512462-0.22576427j -0.01512462+0.22576427j  0.08175089-0.44077141j\n",
      "   0.08175089+0.44077141j -0.09526889-0.05500503j -0.09526889+0.05500503j\n",
      "   0.44844586+0.25285272j  0.44844586-0.25285272j -0.27807507+0.28711822j\n",
      "  -0.27807507-0.28711822j]\n",
      " [-0.06552626+0.34086904j -0.06552626-0.34086904j  0.23888987+0.04878662j\n",
      "   0.23888987-0.04878662j  0.04844488-0.08817096j  0.04844488+0.08817096j\n",
      "   0.07616922+0.08206317j  0.07616922-0.08206317j -0.05148454+0.06072555j\n",
      "  -0.05148454-0.06072555j]\n",
      " [-0.15611312-0.15537037j -0.15611312+0.15537037j -0.14396232+0.15303583j\n",
      "  -0.14396232-0.15303583j  0.04759024+0.04530178j  0.04759024-0.04530178j\n",
      "   0.13220792-0.03480057j  0.13220792+0.03480057j  0.09100802+0.14440161j\n",
      "   0.09100802-0.14440161j]\n",
      " [ 0.13247541+0.35002345j  0.13247541-0.35002345j -0.15989273+0.1499328j\n",
      "  -0.15989273-0.1499328j  -0.51989522-0.01701106j -0.51989522+0.01701106j\n",
      "  -0.45827089-0.12796444j -0.45827089+0.12796444j  0.22932442-0.17323957j\n",
      "   0.22932442+0.17323957j]\n",
      " [-0.33435477-0.03127265j -0.33435477+0.03127265j  0.02210602-0.28361252j\n",
      "   0.02210602+0.28361252j -0.59579969+0.j         -0.59579969-0.j\n",
      "  -0.03704835-0.22823296j -0.03704835+0.22823296j  0.65846689+0.j\n",
      "   0.65846689-0.j        ]\n",
      " [-0.05996823-0.09020731j -0.05996823+0.09020731j -0.2471594 -0.04380808j\n",
      "  -0.2471594 +0.04380808j -0.39834441-0.0887538j  -0.39834441+0.0887538j\n",
      "  -0.11234226+0.05512161j -0.11234226-0.05512161j  0.25511204-0.09592017j\n",
      "   0.25511204+0.09592017j]\n",
      " [ 0.53351001+0.j          0.53351001-0.j          0.30468065+0.03930672j\n",
      "   0.30468065-0.03930672j -0.088475  +0.01353864j -0.088475  -0.01353864j\n",
      "  -0.52763319+0.j         -0.52763319-0.j          0.31984713+0.00809383j\n",
      "   0.31984713-0.00809383j]]\n"
     ]
    }
   ],
   "source": [
    "A = np.random.randn(n, n)\n",
    "\n",
    "true_eigvals, true_eigvec = np.linalg.eig(A)\n",
    "print(true_eigvals)\n",
    "print(np.sort(np.abs(true_eigvals)))\n",
    "print(true_eigvec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.17723423+0.19382756j -0.09721772-0.42693005j -0.12089147-0.20833225j\n",
      " -0.03846834+0.21900876j -0.00075036-0.39424191j -0.12348399+0.04589335j\n",
      "  0.13223092-0.26111013j -0.22654757-0.20870937j -0.05127389+0.0487114j\n",
      "  0.35521168+0.38383698j]\n",
      "(1.3678149826900252-1.2736218961007895j)\n"
     ]
    }
   ],
   "source": [
    "x0 = np.random.randn(n) + 1j * np.random.randn(n)\n",
    "max_eigvec, max_eigval, conv = power_method(A, x0, 4000, 1e-6)\n",
    "print(max_eigvec)\n",
    "print(max_eigval)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "power_method_eigval_conv = np.array([np.linalg.norm(A @ x - x @ (A @ x) * x) for x in conv])\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(power_method_eigval_conv, label=\"Eigval conv\")\n",
    "\n",
    "idx = np.argmax(np.abs(true_eigvals))\n",
    "\n",
    "power_method_eigvec_conv = np.array([np.linalg.norm(x - x[0] / true_eigvec[0, idx] * true_eigvec[:, idx]) for x in conv])\n",
    "plt.plot(power_method_eigvec_conv, label=\"Eigvec conv\")\n",
    "plt.legend(fontsize=20)\n",
    "plt.yscale(\"log\")\n",
    "plt.ylabel(\"Residual norm\", fontsize=20)\n",
    "plt.yticks(fontsize=16)\n",
    "plt.xlabel(\"\\# iterations\", fontsize=20)\n",
    "plt.xticks(fontsize=16)\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.07811809 0.99145656 0.95387387 ... 0.87862328 0.96856575 1.17946532]\n",
      "[0.37000468 0.61691564 1.01553499 ... 1.04216223 1.08150394 0.94061863]\n",
      "1.0\n"
     ]
    }
   ],
   "source": [
    "print(power_method_eigval_conv[1:] / power_method_eigval_conv[:-1])\n",
    "print(power_method_eigvec_conv[1:] / power_method_eigvec_conv[:-1])\n",
    "sorted_abs_eigvals = np.sort(np.abs(true_eigvals))\n",
    "print(sorted_abs_eigvals[-2] / sorted_abs_eigvals[-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Если $\\lambda^*_2 = \\lambda_1$, то степенной метод осциллирует и не сходится! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Степенной метод для максимального сингулярного числа"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def max_singular_value(A, x0, max_iter, eps):\n",
    "    x = x0.copy()\n",
    "    conv_x = []\n",
    "    conv_y = []\n",
    "    for i in range(max_iter):\n",
    "        y = A @ x\n",
    "        y = y / np.linalg.norm(y)\n",
    "        conv_y.append(y.copy())\n",
    "        x = A.T @ y\n",
    "        x = x / np.linalg.norm(x)\n",
    "        conv_x.append(x.copy())\n",
    "        singval = y @ (A @ x)\n",
    "        res = A @ x - singval * y\n",
    "        if np.linalg.norm(res) < eps:\n",
    "            break\n",
    "    return x, y, singval, conv_x, conv_y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "m = 100\n",
    "n = 100\n",
    "max_iter = 20000\n",
    "A = np.random.randn(m, n)\n",
    "x0 = np.random.randn(n)\n",
    "u, v, sigma, conv_x, conv_y = max_singular_value(A, x0, max_iter, 1e-4)\n",
    "U, s, V = np.linalg.svd(A, full_matrices=False)\n",
    "\n",
    "max_eigvec, max_eigval, conv = power_method(A.T @ A, x0, max_iter, 1e-4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20.167164065731537\n",
      "20.16716406840088\n",
      "20.16716406839453\n"
     ]
    }
   ],
   "source": [
    "print(sigma)\n",
    "print(s[0])\n",
    "print(np.sqrt(max_eigval))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.87792426 0.92858724 0.90380411 0.8919542  0.89381115 0.90102153\n",
      " 0.90861505 0.91476577 0.91926174 0.92248534 0.92491195 0.9269275\n",
      " 0.92879654 0.93068174 0.93267189 0.93480442 0.93708116 0.93947902\n",
      " 0.941958   0.94446798 0.94695493 0.94936655 0.95165693 0.95378983\n",
      " 0.95574029 0.95749474 0.95904987 0.96041074 0.96158856 0.96259853\n",
      " 0.96345798 0.96418492 0.96479691 0.96531045 0.9657405  0.96610036\n",
      " 0.9664016  0.9666542  0.96686659 0.96704592 0.96719812 0.96732814\n",
      " 0.96744007 0.96753727 0.96762251 0.96769805 0.96776573 0.96782705\n",
      " 0.96788323 0.96793528 0.96798398 0.96802999 0.96807384 0.96811594\n",
      " 0.96815664 0.96819621 0.96823487 0.96827279 0.96831011 0.96834693\n",
      " 0.96838335 0.96841944 0.96845523 0.96849078 0.96852612 0.96856125\n",
      " 0.96859621 0.968631   0.96866562 0.96870008 0.96873438 0.96876853\n",
      " 0.9688025  0.96883631 0.96886995 0.96890341 0.96893668 0.96896976\n",
      " 0.96900264 0.96903532 0.96906778 0.96910003 0.96913205 0.96916384\n",
      " 0.96919539 0.9692267  0.96925775 0.96928854 0.96931908 0.96934934\n",
      " 0.96937933 0.96940905 0.96943848 0.96946762 0.96949647 0.96952502\n",
      " 0.96955328 0.96958123 0.96960888 0.96963621 0.96966324 0.96968995\n",
      " 0.96971634 0.96974241 0.96976817 0.9697936  0.96981871 0.9698435\n",
      " 0.96986796 0.96989209 0.9699159  0.96993939 0.96996254 0.96998537\n",
      " 0.97000788 0.97003006 0.97005191 0.97007344 0.97009465 0.97011554\n",
      " 0.9701361  0.97015635 0.97017628 0.9701959  0.9702152  0.97023419\n",
      " 0.97025287 0.97027124 0.97028931 0.97030708 0.97032454 0.97034171\n",
      " 0.97035858 0.97037516 0.97039145 0.97040746 0.97042318 0.97043862]\n",
      "0.9571705120785577\n"
     ]
    }
   ],
   "source": [
    "print(np.sqrt(power_method_singval_conv[1:] / power_method_singval_conv[:-1]))\n",
    "print(s[1] / s[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "power_method_singval_conv = np.array([np.linalg.norm(A @ x - y @ (A @ x) * y) for x, y in zip(conv_x, conv_y)])\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(power_method_singval_conv, label=\"Max singval conv\")\n",
    "\n",
    "plt.plot(np.array([np.linalg.norm(A.T @ A @ x - x @ (A.T @ A @ x) * x) for x in conv]), label=\"ATA\")\n",
    "\n",
    "power_method_rightsingvec_conv = np.array([np.linalg.norm(x - x[0] / V[0, 0] * V[0, :].ravel()) for x in conv_x])\n",
    "plt.plot(power_method_rightsingvec_conv, label=\"Right singvec conv\")\n",
    "\n",
    "power_method_leftsingvec_conv = np.array([np.linalg.norm(y - y[0] / U[0, 0] * U[:, 0]) for y in conv_y])\n",
    "plt.plot(power_method_leftsingvec_conv, label=\"Left singvec conv\")\n",
    "\n",
    "plt.legend(fontsize=20)\n",
    "plt.yscale(\"log\")\n",
    "plt.ylabel(\"Residual norm\", fontsize=20)\n",
    "plt.yticks(fontsize=16)\n",
    "plt.xlabel(\"\\# iterations\", fontsize=20)\n",
    "plt.xticks(fontsize=16)\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Другие проблемные случаи для поиска максимального по модулю собственного значения\n",
    "\n",
    "1) $\\lambda_1 = \\lambda_2$\n",
    "\n",
    "2) $\\lambda_1 = -\\lambda_2$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Если $\\lambda_1 = \\lambda_2$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "A = np.random.randn(n, n)\n",
    "Q, _ = np.linalg.qr(A)\n",
    "A = Q @ np.diagflat([2, 2] + list(np.random.rand(n - 2))) @ Q.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.02008642 0.02140786 0.02241596 0.02589456 0.03420331 0.04993936\n",
      " 0.05936717 0.06960574 0.07556917 0.08505168 0.10690188 0.10872478\n",
      " 0.11236629 0.12974489 0.14547573 0.1513387  0.175927   0.17818235\n",
      " 0.18095319 0.1810615  0.18806815 0.18995038 0.20033432 0.21164479\n",
      " 0.23868761 0.25359819 0.26369019 0.27426917 0.27532827 0.27796388\n",
      " 0.28824361 0.31493529 0.36460017 0.3709633  0.37760794 0.38150488\n",
      " 0.38527079 0.39723203 0.40469208 0.40921147 0.41665167 0.43333612\n",
      " 0.44907336 0.45176696 0.47114553 0.47905631 0.49409229 0.50028761\n",
      " 0.50360713 0.50819353 0.54071795 0.56909787 0.56954551 0.59165629\n",
      " 0.59588949 0.5981202  0.60303168 0.614568   0.6257656  0.62651864\n",
      " 0.62851077 0.63001438 0.63556431 0.64623187 0.64932541 0.65346986\n",
      " 0.66692136 0.69166261 0.70701347 0.72458438 0.73935829 0.74732051\n",
      " 0.75343685 0.75740952 0.76694906 0.7767082  0.77676455 0.78548952\n",
      " 0.78901953 0.79233343 0.81065026 0.83086734 0.83149841 0.84807786\n",
      " 0.85035599 0.85671053 0.87874804 0.88709514 0.89519947 0.92259366\n",
      " 0.92262683 0.93329009 0.94251582 0.95640791 0.96852825 0.97352556\n",
      " 0.99288073 0.99352106 2.         2.        ]\n",
      "[0.02008642 0.02140786 0.02241596 0.02589456 0.03420331 0.04993936\n",
      " 0.05936717 0.06960574 0.07556917 0.08505168 0.10690188 0.10872478\n",
      " 0.11236629 0.12974489 0.14547573 0.1513387  0.175927   0.17818235\n",
      " 0.18095319 0.1810615  0.18806815 0.18995038 0.20033432 0.21164479\n",
      " 0.23868761 0.25359819 0.26369019 0.27426917 0.27532827 0.27796388\n",
      " 0.28824361 0.31493529 0.36460017 0.3709633  0.37760794 0.38150488\n",
      " 0.38527079 0.39723203 0.40469208 0.40921147 0.41665167 0.43333612\n",
      " 0.44907336 0.45176696 0.47114553 0.47905631 0.49409229 0.50028761\n",
      " 0.50360713 0.50819353 0.54071795 0.56909787 0.56954551 0.59165629\n",
      " 0.59588949 0.5981202  0.60303168 0.614568   0.6257656  0.62651864\n",
      " 0.62851077 0.63001438 0.63556431 0.64623187 0.64932541 0.65346986\n",
      " 0.66692136 0.69166261 0.70701347 0.72458438 0.73935829 0.74732051\n",
      " 0.75343685 0.75740952 0.76694906 0.7767082  0.77676455 0.78548952\n",
      " 0.78901953 0.79233343 0.81065026 0.83086734 0.83149841 0.84807786\n",
      " 0.85035599 0.85671053 0.87874804 0.88709514 0.89519947 0.92259366\n",
      " 0.92262683 0.93329009 0.94251582 0.95640791 0.96852825 0.97352556\n",
      " 0.99288073 0.99352106 2.         2.        ]\n",
      "[[-6.44600234e-02  4.37701701e-02 -1.71601048e-01 ... -6.64577529e-02\n",
      "  -2.28983499e-16  1.33339276e-01]\n",
      " [-9.82759255e-02  1.00660706e-01  4.36029281e-02 ... -1.16130884e-01\n",
      "   6.54604609e-02 -3.31185136e-02]\n",
      " [ 2.17259832e-02 -2.71370711e-02 -1.42623490e-01 ...  1.94684048e-01\n",
      "  -9.66705370e-02  1.02235547e-01]\n",
      " ...\n",
      " [-3.33060149e-02  4.00050793e-03 -5.27945383e-03 ... -6.34533859e-02\n",
      "  -2.87529090e-02  2.76203765e-02]\n",
      " [-1.21196836e-01 -2.44273364e-02 -7.53528370e-02 ...  6.35111497e-02\n",
      "   1.01837760e-02 -1.08034184e-02]\n",
      " [ 1.71052201e-02  3.71702473e-02  1.59794016e-02 ... -1.01377464e-02\n",
      "  -1.46379900e-01 -6.27261804e-02]]\n"
     ]
    }
   ],
   "source": [
    "true_eigvals, true_eigvec = np.linalg.eigh(A)\n",
    "print(true_eigvals)\n",
    "print(np.abs(true_eigvals))\n",
    "print(true_eigvec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.06127436e-02  6.78888003e-02 -1.04501100e-01  1.07689971e-02\n",
      "  3.27838598e-02 -6.45828201e-02  1.10092206e-02  1.07226201e-01\n",
      " -6.24700642e-02 -8.27976260e-02  7.38003878e-02  6.79558817e-02\n",
      "  2.80826433e-01 -5.28449215e-02 -1.76477577e-01 -5.13408822e-02\n",
      "  7.11447167e-02 -1.04190488e-01 -1.12903929e-01 -1.85324585e-02\n",
      "  1.03811522e-01  7.40831608e-02  6.68314129e-02  8.87054512e-02\n",
      " -1.76858509e-01 -1.53880921e-02  1.26335389e-01 -1.66486492e-01\n",
      " -7.72124824e-02 -1.12636209e-01 -1.66111376e-01 -1.39314748e-01\n",
      "  9.50481611e-02  1.72905979e-01  6.96063522e-03  9.26812451e-02\n",
      "  1.84284989e-01  3.79948957e-02 -1.97928698e-02 -1.71573244e-01\n",
      "  7.92309132e-02 -1.82124878e-01 -1.33931843e-02  3.97772832e-02\n",
      " -5.27815050e-02  6.07548893e-02 -1.62606374e-03  6.98443678e-02\n",
      " -5.76840442e-03 -2.68783100e-02 -5.63808117e-02  4.47175970e-02\n",
      "  2.23177621e-04 -1.01147130e-01 -6.14508403e-03  3.60008451e-02\n",
      " -7.79715322e-03  1.30845967e-01  1.41514963e-02  2.91640220e-02\n",
      " -9.21166473e-02  9.53634504e-05 -1.54012337e-01 -1.17271313e-01\n",
      "  1.43796261e-01 -1.22149981e-01 -2.06994888e-02  1.72196908e-02\n",
      "  1.80696679e-01 -9.50273695e-02  4.84595174e-02  7.33668964e-02\n",
      "  1.08936201e-01 -6.65839702e-02  1.57829474e-01  1.69268830e-01\n",
      " -7.78051226e-02  1.98014956e-02 -1.11570166e-01  9.78027656e-02\n",
      " -1.18741877e-01 -1.16193270e-01 -2.00709004e-01 -5.51667168e-02\n",
      "  2.34582165e-02 -4.48703043e-02 -5.34046752e-02 -2.78716412e-02\n",
      "  1.73556361e-01  1.48162319e-01 -1.22710085e-01  6.20304710e-02\n",
      " -1.08842866e-01  3.26126994e-02 -5.84148828e-02  1.13646196e-01\n",
      "  5.72731993e-02 -3.08600806e-02  1.10113002e-02 -1.40922998e-01] 1.0\n",
      "1.9999999999996836\n"
     ]
    }
   ],
   "source": [
    "x0 = np.random.randn(n)\n",
    "max_eigvec, max_eigval, conv = power_method(A, x0, 1000, 1e-6)\n",
    "print(max_eigvec, np.linalg.norm(max_eigvec))\n",
    "print(max_eigval)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "power_method_eigval_conv = np.array([np.linalg.norm(A @ x - x @ (A @ x) * x) for x in conv])\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(power_method_eigval_conv, linewidth=4, label=\"Eigval conv\")\n",
    "\n",
    "idx = np.argmax(np.abs(true_eigvals))\n",
    "\n",
    "power_method_eigvec_conv = np.array([np.linalg.norm(x - x[0] / true_eigvec[0, idx] * true_eigvec[:, idx]) for x in conv])\n",
    "plt.plot(power_method_eigvec_conv, linewidth=4, label=\"Eigvec conv\")\n",
    "plt.legend(fontsize=20)\n",
    "plt.yscale(\"log\")\n",
    "plt.ylabel(\"Residual norm\", fontsize=20)\n",
    "plt.yticks(fontsize=16)\n",
    "plt.xlabel(\"\\# iterations\", fontsize=20)\n",
    "plt.xticks(fontsize=16)\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.9968275  -0.07959227]\n"
     ]
    }
   ],
   "source": [
    "alpha = np.linalg.lstsq(true_eigvec[:, n-2:], max_eigvec, rcond=None)[0]\n",
    "print(alpha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 169,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy = 5.598148227226629e-07\n"
     ]
    }
   ],
   "source": [
    "print(\"Accuracy = {}\".format(np.linalg.norm(true_eigvec[:, n-2:] @ alpha - max_eigvec)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Если $\\lambda_1 = -\\lambda_2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "A = np.random.randn(n, n)\n",
    "Q, _ = np.linalg.qr(A)\n",
    "A = Q @ np.diagflat([2, -2] + list(np.random.rand(n - 2))) @ Q.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-2.          0.02758757  0.03385891  0.03695993  0.05017623  0.05048221\n",
      "  0.05067216  0.06322825  0.0636333   0.0698557   0.08038562  0.08726109\n",
      "  0.08860725  0.09530253  0.09613168  0.09621899  0.12429812  0.15448181\n",
      "  0.17512833  0.17692935  0.17897333  0.18348431  0.18415076  0.18783721\n",
      "  0.1889341   0.19599802  0.20729099  0.21934144  0.23128556  0.24548163\n",
      "  0.24649978  0.2765182   0.27754471  0.28338208  0.28949609  0.30314122\n",
      "  0.30685771  0.31579599  0.3377595   0.34257715  0.36070068  0.3678631\n",
      "  0.36920737  0.37394591  0.37694607  0.38755859  0.41592633  0.42108433\n",
      "  0.42261864  0.4240153   0.42783761  0.44114719  0.44378146  0.44461848\n",
      "  0.46744859  0.47149639  0.48665376  0.49177645  0.52549973  0.52912111\n",
      "  0.56032442  0.56300716  0.56520041  0.56710325  0.56837414  0.60441289\n",
      "  0.62137366  0.65854602  0.68552649  0.69191354  0.708202    0.72745894\n",
      "  0.73910831  0.7416543   0.74287446  0.74787385  0.74798008  0.76121617\n",
      "  0.76450321  0.78961834  0.79731004  0.81919919  0.82935245  0.83501001\n",
      "  0.87012865  0.8776473   0.87975432  0.8925912   0.89437461  0.90957571\n",
      "  0.9118236   0.91194144  0.93085157  0.94171299  0.96149374  0.96779324\n",
      "  0.96917103  0.98687508  0.99880419  2.        ]\n",
      "[2.         0.02758757 0.03385891 0.03695993 0.05017623 0.05048221\n",
      " 0.05067216 0.06322825 0.0636333  0.0698557  0.08038562 0.08726109\n",
      " 0.08860725 0.09530253 0.09613168 0.09621899 0.12429812 0.15448181\n",
      " 0.17512833 0.17692935 0.17897333 0.18348431 0.18415076 0.18783721\n",
      " 0.1889341  0.19599802 0.20729099 0.21934144 0.23128556 0.24548163\n",
      " 0.24649978 0.2765182  0.27754471 0.28338208 0.28949609 0.30314122\n",
      " 0.30685771 0.31579599 0.3377595  0.34257715 0.36070068 0.3678631\n",
      " 0.36920737 0.37394591 0.37694607 0.38755859 0.41592633 0.42108433\n",
      " 0.42261864 0.4240153  0.42783761 0.44114719 0.44378146 0.44461848\n",
      " 0.46744859 0.47149639 0.48665376 0.49177645 0.52549973 0.52912111\n",
      " 0.56032442 0.56300716 0.56520041 0.56710325 0.56837414 0.60441289\n",
      " 0.62137366 0.65854602 0.68552649 0.69191354 0.708202   0.72745894\n",
      " 0.73910831 0.7416543  0.74287446 0.74787385 0.74798008 0.76121617\n",
      " 0.76450321 0.78961834 0.79731004 0.81919919 0.82935245 0.83501001\n",
      " 0.87012865 0.8776473  0.87975432 0.8925912  0.89437461 0.90957571\n",
      " 0.9118236  0.91194144 0.93085157 0.94171299 0.96149374 0.96779324\n",
      " 0.96917103 0.98687508 0.99880419 2.        ]\n",
      "[[ 0.01985026 -0.07192831  0.08834162 ... -0.00570495  0.08829013\n",
      "  -0.14307232]\n",
      " [ 0.11508445 -0.07831884 -0.00736285 ...  0.17000267  0.06256991\n",
      "   0.05146019]\n",
      " [-0.25367261  0.1303228  -0.04841141 ... -0.03171548  0.01816187\n",
      "   0.27931397]\n",
      " ...\n",
      " [-0.03803362 -0.00082402  0.13739591 ... -0.04590969  0.27215806\n",
      "  -0.0839057 ]\n",
      " [ 0.08599804  0.12430343 -0.02422063 ...  0.08625126  0.18132368\n",
      "  -0.02830516]\n",
      " [-0.08501145  0.08773266 -0.15500092 ... -0.08442033 -0.05406858\n",
      "   0.12817195]]\n"
     ]
    }
   ],
   "source": [
    "true_eigvals, true_eigvec = np.linalg.eigh(A)\n",
    "print(true_eigvals)\n",
    "print(np.abs(true_eigvals))\n",
    "print(true_eigvec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.13016163  0.08416795  0.18842993 -0.0906004  -0.0933216   0.0701698\n",
      "  0.10180757 -0.17530844 -0.06607556  0.02309969 -0.03565756  0.06029751\n",
      " -0.13993817  0.11978141 -0.10805633 -0.03575319 -0.08086227  0.07069391\n",
      "  0.13159286  0.0226421   0.0146758  -0.07700928 -0.02166633 -0.2100961\n",
      " -0.04992481 -0.06708214 -0.13115851 -0.01962476  0.13762516 -0.17926883\n",
      "  0.13710191 -0.0922936   0.00256794 -0.05973978 -0.01916618 -0.03921299\n",
      "  0.01263338  0.04494502  0.07652736  0.035351   -0.13459893  0.08107362\n",
      " -0.02021443 -0.02940069  0.02293267 -0.01394442  0.0062745  -0.22208237\n",
      " -0.02394064 -0.05059291  0.12431545 -0.03729898 -0.15965682  0.17744071\n",
      " -0.01132518 -0.15139785  0.07420981  0.03745272  0.04182613  0.13295984\n",
      "  0.11460563  0.05050747  0.17280734 -0.14735083 -0.10086552 -0.00735431\n",
      " -0.2184886  -0.16727563 -0.10140203 -0.17465816  0.01259542  0.11536362\n",
      " -0.14247907 -0.15876815 -0.073401   -0.05817324 -0.14719672 -0.05566404\n",
      "  0.00820563  0.14594863 -0.05581049 -0.0414607  -0.1031092   0.05996491\n",
      " -0.05549855  0.06362265 -0.13053461  0.00951447  0.07493481 -0.0543385\n",
      " -0.00757839 -0.06752812 -0.0565648   0.02521422 -0.12570456  0.10888286\n",
      "  0.08436761 -0.0915147  -0.00067023  0.09606096]\n",
      "1.6264394847295924\n"
     ]
    }
   ],
   "source": [
    "x0 = np.random.randn(n)\n",
    "max_eigvec, max_eigval, conv = power_method(A, x0, 1000, 1e-6)\n",
    "print(max_eigvec)\n",
    "print(max_eigval)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([18.97809967,  3.92722686,  6.42246428, ...,  6.92851027,\n",
       "        6.92851027,  6.92851027])"
      ]
     },
     "execution_count": 177,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(conv[-1] - conv[-2])\n",
    "power_method_eigvec_conv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "power_method_eigval_conv = np.array([np.linalg.norm(A @ x - x @ (A @ x) * x) for x in conv])\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(power_method_eigval_conv, linewidth=4, label=\"Eigval conv\")\n",
    "\n",
    "idx = np.argmax(np.abs(true_eigvals))\n",
    "\n",
    "power_method_eigvec_conv = np.array([np.linalg.norm(x - x[0] / true_eigvec[0, idx] * true_eigvec[:, idx]) for x in conv])\n",
    "plt.plot(power_method_eigvec_conv, linewidth=4, label=\"Eigvec conv\")\n",
    "plt.legend(fontsize=20)\n",
    "plt.yscale(\"log\")\n",
    "plt.ylabel(\"Residual norm\", fontsize=20)\n",
    "plt.yticks(fontsize=16)\n",
    "plt.xlabel(\"\\# iterations\", fontsize=20)\n",
    "plt.xticks(fontsize=16)\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Блочный степенной метод\n",
    "\n",
    "- Ищем $k$ cтарших собственных значения и вектора\n",
    "- Этапы аналогичны степенному методу для максимального по модулю собственного значения\n",
    "    - Умножение матрицы на набор векторов\n",
    "    - Аналог нормализации для матриц?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def block_power_method(A, x0, max_iter, eps):\n",
    "    x = x0.copy()\n",
    "    conv_vec = [x]\n",
    "    conv_val = [np.einsum('ik,ij,jk->k',x, A, x)]\n",
    "    for i in range(max_iter):\n",
    "        x = A @ x\n",
    "        x, _ = np.linalg.qr(x)\n",
    "        conv_vec.append(x)\n",
    "        eigval = np.einsum('ik,ij,jk->k', x, A, x)\n",
    "        conv_val.append(eigval)\n",
    "        res = A @ x - (eigval[:, np.newaxis] * x.T).T\n",
    "        if np.linalg.norm(res) < eps:\n",
    "            break\n",
    "    return x, eigval, conv_vec, conv_val"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Немного про einsum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 186,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.21412322602367861 -0.21412322602367717\n",
      "[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
      " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
      " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
      " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
      " 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
      " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
      " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
      " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
      " 0. 0. 0. 0.]\n"
     ]
    }
   ],
   "source": [
    "A = np.random.randn(n, n)\n",
    "print(np.trace(A), np.einsum('ii', A))\n",
    "print(np.diag(A) - np.einsum(\"ii->i\", A))\n",
    "print(np.einsum(\"ij->j\", A) - np.sum(A, axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 187,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-4.44089210e-16  3.55271368e-15  4.44089210e-15  1.77635684e-15\n",
      " -3.55271368e-15  4.44089210e-16 -1.77635684e-15 -1.77635684e-15\n",
      " -1.55431223e-15  0.00000000e+00  3.77475828e-15  1.77635684e-15\n",
      " -3.55271368e-15  7.10542736e-15  0.00000000e+00  0.00000000e+00\n",
      "  3.55271368e-15  0.00000000e+00  0.00000000e+00 -2.66453526e-15\n",
      " -3.55271368e-15  4.99600361e-16 -3.55271368e-15  5.32907052e-15\n",
      "  0.00000000e+00 -1.99840144e-15  1.33226763e-15  3.55271368e-15\n",
      "  3.55271368e-15  3.55271368e-15 -4.44089210e-16  6.49480469e-15\n",
      "  2.66453526e-15 -1.77635684e-15 -3.55271368e-15  0.00000000e+00\n",
      " -3.55271368e-15  5.32907052e-15  1.77635684e-15  0.00000000e+00\n",
      "  0.00000000e+00  1.77635684e-15  1.77635684e-15  1.77635684e-15\n",
      "  1.77635684e-15 -4.44089210e-16 -3.55271368e-15 -4.44089210e-16\n",
      "  1.11022302e-15 -2.66453526e-15  3.55271368e-15  2.66453526e-15\n",
      "  3.88578059e-15  5.32907052e-15  1.77635684e-15  0.00000000e+00\n",
      "  8.88178420e-16  5.32907052e-15 -3.55271368e-15  4.44089210e-16\n",
      " -1.77635684e-15  0.00000000e+00 -2.22044605e-15  0.00000000e+00\n",
      "  3.55271368e-15  1.06581410e-14 -2.66453526e-15 -1.77635684e-15\n",
      " -4.44089210e-15 -2.66453526e-15 -2.44249065e-15 -6.21724894e-15\n",
      " -1.99840144e-15 -8.88178420e-16 -1.77635684e-15  2.38697950e-15\n",
      " -3.55271368e-15  7.10542736e-15  4.44089210e-15  0.00000000e+00\n",
      "  0.00000000e+00  0.00000000e+00  1.99840144e-15 -2.99760217e-15\n",
      "  1.77635684e-15  7.10542736e-15  2.66453526e-15  4.44089210e-16\n",
      " -3.55271368e-15 -3.55271368e-15 -1.33226763e-15  8.88178420e-16\n",
      "  2.66453526e-15 -1.77635684e-15 -3.55271368e-15  3.55271368e-15\n",
      " -7.10542736e-15  3.55271368e-15  3.55271368e-15  1.77635684e-15]\n"
     ]
    }
   ],
   "source": [
    "x = np.random.randn(n)\n",
    "print(A @ x - np.einsum('ij,j', A, x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 8.88178420e-16 -1.77635684e-15 -4.21884749e-15  0.00000000e+00\n",
      "  0.00000000e+00  1.77635684e-15  8.88178420e-16 -1.77635684e-15\n",
      "  0.00000000e+00  8.88178420e-16  0.00000000e+00  1.77635684e-15\n",
      "  0.00000000e+00  0.00000000e+00 -2.66453526e-15 -8.88178420e-16\n",
      " -1.77635684e-15 -7.77156117e-16  0.00000000e+00 -1.77635684e-15\n",
      "  0.00000000e+00 -1.77635684e-15 -1.77635684e-15  0.00000000e+00\n",
      " -1.77635684e-15 -6.66133815e-16 -1.77635684e-15  0.00000000e+00\n",
      "  0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
      "  1.77635684e-15  0.00000000e+00  1.77635684e-15 -7.10542736e-15\n",
      " -8.88178420e-16 -1.77635684e-15  8.88178420e-16 -8.88178420e-16\n",
      "  0.00000000e+00  4.44089210e-15  0.00000000e+00 -2.66453526e-15\n",
      " -1.77635684e-15 -8.88178420e-16 -8.88178420e-16 -8.88178420e-16\n",
      "  2.22044605e-15  3.55271368e-15 -8.88178420e-16  1.66533454e-15\n",
      " -7.10542736e-15 -7.10542736e-15  0.00000000e+00 -1.97064587e-15\n",
      "  0.00000000e+00 -4.44089210e-16 -4.44089210e-16 -1.77635684e-15\n",
      "  3.55271368e-15 -1.77635684e-15  0.00000000e+00  4.44089210e-16\n",
      "  0.00000000e+00 -1.77635684e-15  1.33226763e-15 -1.77635684e-15\n",
      " -1.33226763e-15 -8.88178420e-16 -3.55271368e-15  3.55271368e-15\n",
      " -1.11022302e-15  8.88178420e-16 -3.55271368e-15  0.00000000e+00\n",
      "  1.77635684e-15  0.00000000e+00 -1.77635684e-15 -8.88178420e-16\n",
      "  3.10862447e-15  8.88178420e-16 -1.77635684e-15  0.00000000e+00\n",
      "  1.77635684e-15  0.00000000e+00 -1.77635684e-15  1.77635684e-15\n",
      "  8.88178420e-16  8.88178420e-16 -8.88178420e-16  0.00000000e+00\n",
      " -1.11022302e-15  1.77635684e-15  0.00000000e+00  3.55271368e-15\n",
      "  8.88178420e-16 -2.22044605e-16 -2.66453526e-15  0.00000000e+00]\n"
     ]
    }
   ],
   "source": [
    "B = np.random.randn(n, n)\n",
    "print(np.diag(A @ B) - np.einsum('ij,ji->i', A, B))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Более подробное об этой операции см. [тут](https://obilaniu6266h16.wordpress.com/2016/02/04/einstein-summation-in-numpy/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Вернёмся к блочному степенному методу"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0.13667257  0.24594346  1.49671866  2.00019072  5.5754419  12.85373375\n",
      " 13.06338092 20.49433594 25.89913379 39.15712683]\n",
      "[[ 0.60426692 -0.18769617 -0.13409066  0.44706793 -0.09510907 -0.33279642\n",
      "  -0.09952021  0.48463227  0.08658801 -0.09855061]\n",
      " [-0.21655158 -0.09545903  0.55718089  0.63398018  0.063534    0.08658202\n",
      "  -0.34175311 -0.23794884  0.21529564 -0.01764962]\n",
      " [ 0.34313366  0.32540598 -0.35033254 -0.06019388 -0.03471395  0.4514748\n",
      "  -0.51366779 -0.23532642  0.31285171 -0.16694366]\n",
      " [-0.34695034  0.02255482 -0.07764918 -0.06958919  0.24675194 -0.15460022\n",
      "  -0.29503492  0.24538339 -0.20408131 -0.77107013]\n",
      " [-0.27895266  0.0121989  -0.08370454  0.05006053  0.21891585  0.42996461\n",
      "  -0.23086884  0.6670614  -0.03791468  0.42428943]\n",
      " [ 0.39199732  0.099514    0.55506228 -0.12198374  0.03475056  0.5024397\n",
      "   0.30084755  0.19819045 -0.1801961  -0.31232725]\n",
      " [-0.30312827  0.27086395 -0.26898536  0.43061804 -0.58145892  0.23678601\n",
      "   0.36249207  0.09535418 -0.01635814 -0.20503258]\n",
      " [ 0.04945376 -0.72450566 -0.2186527   0.06952121 -0.15901101  0.34764544\n",
      "  -0.13369842 -0.21441538 -0.45609077 -0.044652  ]\n",
      " [ 0.07272816  0.36801999  0.22304146 -0.07025758 -0.42589425 -0.19801883\n",
      "  -0.43921801  0.01442987 -0.59394742  0.19518372]\n",
      " [-0.13694294 -0.32479787  0.24040937 -0.42088731 -0.5752647  -0.02382746\n",
      "  -0.19079424  0.23107447  0.46006179 -0.08864681]]\n"
     ]
    }
   ],
   "source": [
    "block_size = 3\n",
    "n = 10\n",
    "A = np.random.randn(n, n)\n",
    "A = A.T @ A\n",
    "true_eigvals, true_eigvec = np.linalg.eigh(A)\n",
    "print(true_eigvals)\n",
    "print(true_eigvec)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 192,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.09855061 -0.08658806  0.48463226]\n",
      " [-0.01764962 -0.21529562 -0.23794887]\n",
      " [-0.16694366 -0.31285169 -0.23532645]\n",
      " [-0.77107013  0.20408128  0.24538341]\n",
      " [ 0.42428943  0.03791461  0.66706141]\n",
      " [-0.31232725  0.18019608  0.19819047]\n",
      " [-0.20503258  0.01635813  0.09535418]\n",
      " [-0.044652    0.4560908  -0.21441533]\n",
      " [ 0.19518372  0.59394742  0.01442994]\n",
      " [-0.08864681 -0.46006181  0.23107442]]\n",
      "[39.15712683 25.89913379 20.49433594]\n",
      "[[-0.09855061  0.08658801  0.48463227]\n",
      " [-0.01764962  0.21529564 -0.23794884]\n",
      " [-0.16694366  0.31285171 -0.23532642]\n",
      " [-0.77107013 -0.20408131  0.24538339]\n",
      " [ 0.42428943 -0.03791468  0.6670614 ]\n",
      " [-0.31232725 -0.1801961   0.19819045]\n",
      " [-0.20503258 -0.01635814  0.09535418]\n",
      " [-0.044652   -0.45609077 -0.21441538]\n",
      " [ 0.19518372 -0.59394742  0.01442987]\n",
      " [-0.08864681  0.46006179  0.23107447]]\n"
     ]
    }
   ],
   "source": [
    "x0 = np.random.randn(n, block_size)\n",
    "max_eigvec, max_eigval, conv_vec, conv_val = block_power_method(A, x0, 500, 1e-6)\n",
    "print(max_eigvec)\n",
    "print(max_eigval)\n",
    "print(true_eigvec[:, n-block_size:n][:, ::-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "power_method_eigval_conv = np.array([np.linalg.norm(A @ x - lam * x) for x, lam in zip(conv_vec, conv_val)])\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(power_method_eigval_conv, linewidth=4, label=\"Eigval conv\")\n",
    "\n",
    "idx = np.argsort(np.abs(true_eigvals))\n",
    "\n",
    "plt.legend(fontsize=20)\n",
    "plt.yscale(\"log\")\n",
    "plt.ylabel(\"Residual norm\", fontsize=20)\n",
    "plt.yticks(fontsize=16)\n",
    "plt.xlabel(\"\\# iterations\", fontsize=20)\n",
    "plt.xticks(fontsize=16)\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.02150471 0.49504562 0.57330245 0.65194056 0.70818045 0.75011071\n",
      " 0.77570554 0.78723868 0.7907368  0.79095939 0.79031391 0.78970421\n",
      " 0.78935329 0.78924262 0.78929634 0.78944435 0.78963706 0.78984388\n",
      " 0.79004788 0.79024084 0.79041964 0.79058386 0.79073442 0.79087275\n",
      " 0.79100034 0.7911186  0.79122874 0.79133175 0.79142846 0.79151954\n",
      " 0.79160552 0.79168684 0.79176386 0.79183688 0.79190616 0.79197192\n",
      " 0.79203436 0.79209364 0.79214994 0.79220341 0.79225417 0.79230237\n",
      " 0.79234813 0.79239155 0.79243276 0.79247187 0.79250896 0.79254415\n",
      " 0.79257752 0.79260915 0.79263915 0.79266758 0.79269453 0.79272007\n",
      " 0.79274427 0.7927672  0.79278892 0.79280949 0.79282897 0.79284742\n",
      " 0.7928649  0.79288144 0.7928971  0.79291193 0.79292597 0.79293925\n",
      " 0.79295183 0.79296373 0.79297499]\n",
      "0.7931716980054303\n",
      "49.29861083650784 26.489051977195768 17.45962262942466\n"
     ]
    }
   ],
   "source": [
    "print(power_method_eigval_conv[1:] / power_method_eigval_conv[:-1])\n",
    "print(true_eigvals[-4] / true_eigvals[-3])\n",
    "print(true_eigvals[-1], true_eigvals[-2], true_eigvals[-3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Несимметричный случай"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "A = np.random.randn(n, n)\n",
    "\n",
    "# A = np.random.randn(n, n)\n",
    "# Q, _ = np.linalg.qr(A)\n",
    "# A = Q @ np.diagflat([2, 2, 2] + list(np.random.rand(n - 3))) @ Q.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 3.06838598+0.j         -2.31344654+1.18200744j -2.31344654-1.18200744j\n",
      "  0.75305127+1.90093489j  0.75305127-1.90093489j -0.88288068+1.48872998j\n",
      " -0.88288068-1.48872998j  0.78706991+0.36474996j  0.78706991-0.36474996j\n",
      " -0.84075908+0.j        ]\n",
      "[0.84075908 0.86748002 0.86748002 1.73083657 1.73083657 2.04466127\n",
      " 2.04466127 2.59791772 2.59791772 3.06838598]\n",
      "[[-0.23429+0.j      -0.21933+0.20767j -0.21933-0.20767j  0.16437+0.09736j\n",
      "   0.16437-0.09736j  0.29776-0.17504j  0.29776+0.17504j  0.10549-0.30279j\n",
      "   0.10549+0.30279j -0.04317+0.j     ]\n",
      " [ 0.5203 +0.j      -0.36054-0.13962j -0.36054+0.13962j  0.24173+0.25342j\n",
      "   0.24173-0.25342j  0.19973-0.03282j  0.19973+0.03282j  0.23972-0.10406j\n",
      "   0.23972+0.10406j -0.20022+0.j     ]\n",
      " [ 0.13478+0.j       0.46095+0.j       0.46095-0.j       0.02521+0.11215j\n",
      "   0.02521-0.11215j -0.17194+0.01238j -0.17194-0.01238j -0.23955-0.19038j\n",
      "  -0.23955+0.19038j  0.19383+0.j     ]\n",
      " [-0.38962+0.j       0.04623-0.00466j  0.04623+0.00466j -0.18016-0.03476j\n",
      "  -0.18016+0.03476j -0.02962-0.1011j  -0.02962+0.1011j   0.00894+0.26515j\n",
      "   0.00894-0.26515j -0.42075+0.j     ]\n",
      " [ 0.27777+0.j       0.0743 +0.03884j  0.0743 -0.03884j  0.18003+0.18155j\n",
      "   0.18003-0.18155j  0.46459+0.j       0.46459-0.j       0.53172+0.j\n",
      "   0.53172-0.j      -0.42576+0.j     ]\n",
      " [-0.36595+0.j       0.23932+0.23779j  0.23932-0.23779j -0.03521+0.28175j\n",
      "  -0.03521-0.28175j -0.36147+0.06221j -0.36147-0.06221j -0.05535-0.31479j\n",
      "  -0.05535+0.31479j  0.47026+0.j     ]\n",
      " [-0.28617+0.j       0.18925-0.41834j  0.18925+0.41834j -0.08346+0.4433j\n",
      "  -0.08346-0.4433j   0.09509+0.43968j  0.09509-0.43968j  0.29458+0.04376j\n",
      "   0.29458-0.04376j -0.36597+0.j     ]\n",
      " [-0.31963+0.j       0.10231+0.03848j  0.10231-0.03848j -0.57147+0.j\n",
      "  -0.57147-0.j      -0.14715-0.16283j -0.14715+0.16283j  0.1065 +0.28891j\n",
      "   0.1065 -0.28891j -0.34372+0.j     ]\n",
      " [-0.00916+0.j      -0.35768-0.01928j -0.35768+0.01928j  0.04371-0.15938j\n",
      "   0.04371+0.15938j -0.23933-0.17222j -0.23933+0.17222j -0.15763-0.23765j\n",
      "  -0.15763+0.23765j  0.2981 +0.j     ]\n",
      " [-0.33046+0.j      -0.14161-0.22949j -0.14161+0.22949j  0.20412-0.22123j\n",
      "   0.20412+0.22123j  0.15719-0.2939j   0.15719+0.2939j   0.02664-0.12025j\n",
      "   0.02664+0.12025j -0.01   +0.j     ]]\n"
     ]
    }
   ],
   "source": [
    "true_eigvals, true_eigvec = np.linalg.eig(A)\n",
    "block_size = 3\n",
    "print(true_eigvals)\n",
    "print(np.sort(np.abs(true_eigvals)))\n",
    "print(true_eigvec.round(5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.23428636 -0.48939338  0.09687676]\n",
      " [ 0.52030405  0.00260625  0.39011415]\n",
      " [ 0.13477928  0.35450994 -0.51362813]\n",
      " [-0.38962469 -0.00839508  0.03998234]\n",
      " [ 0.2777723   0.0333413  -0.17276611]\n",
      " [-0.36594661 -0.21346735 -0.38334   ]\n",
      " [-0.28616996  0.70558098  0.23455394]\n",
      " [-0.31963197 -0.02071723 -0.07242365]\n",
      " [-0.00916342 -0.23530553  0.39499858]\n",
      " [-0.33046114  0.1855187   0.42418285]]\n",
      "[ 3.06838598 -2.59194361 -2.03494946]\n",
      "[[-0.04317115+0.j          0.10548865+0.30279143j  0.10548865-0.30279143j]\n",
      " [-0.20021665+0.j          0.23972272+0.10406348j  0.23972272-0.10406348j]\n",
      " [ 0.19382538+0.j         -0.23954693+0.19038166j -0.23954693-0.19038166j]\n",
      " [-0.4207494 +0.j          0.00893826-0.26514632j  0.00893826+0.26514632j]\n",
      " [-0.42575704+0.j          0.53172276-0.j          0.53172276+0.j        ]\n",
      " [ 0.47025627+0.j         -0.055354  +0.31478542j -0.055354  -0.31478542j]\n",
      " [-0.36597013+0.j          0.29458327-0.0437575j   0.29458327+0.0437575j ]\n",
      " [-0.34371663+0.j          0.10650474-0.28890641j  0.10650474+0.28890641j]\n",
      " [ 0.29810382+0.j         -0.15763469+0.23764747j -0.15763469-0.23764747j]\n",
      " [-0.01000207+0.j          0.02663951+0.12025405j  0.02663951-0.12025405j]]\n"
     ]
    }
   ],
   "source": [
    "x0 = np.random.randn(n, block_size) #+ 1j * np.random.randn(n, block_size)\n",
    "max_eigvec, max_eigval, conv_vec, conv_val = block_power_method(A, x0, 500, 1e-6)\n",
    "print(max_eigvec)\n",
    "print(max_eigval)\n",
    "print(true_eigvec[:, n-block_size:n][:, ::-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "power_method_eigval_conv = np.array([np.linalg.norm(A @ x - lam * x) for x, lam in zip(conv_vec, conv_val)])\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(power_method_eigval_conv, linewidth=4, label=\"Eigval conv\")\n",
    "\n",
    "idx = np.argsort(np.abs(true_eigvals))\n",
    "\n",
    "plt.legend(fontsize=20)\n",
    "plt.yscale(\"log\")\n",
    "plt.ylabel(\"Residual norm\", fontsize=20)\n",
    "plt.yticks(fontsize=16)\n",
    "plt.xlabel(\"\\# iterations\", fontsize=20)\n",
    "plt.xticks(fontsize=16)\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### Какие собственные значения удаётся восстановить, а какие нет?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Резюме\n",
    "\n",
    "- Сходимость степенного метода\n",
    "- Аналог степенного метода для задачи поиска максимального сингулярного значения\n",
    "- Блочный степенной метод \n",
    "- Операция ```einsum``` и эффективный способ вычисления диагонали произведения матриц"
   ]
  }
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